Methods and apparatus to determine probabilistic media viewing metrics

ABSTRACT

Methods and apparatus to determine probabilistic media viewing metrics are disclosed herein. An example apparatus for determining a viewing metric for media to be viewed by a plurality of panelists includes a probability identifier to identify a probability for respective ones of the panelists with respect to the panelists viewing the media. The probability identifier is to identify the probability based on viewing data for the respective ones of the panelists. The example apparatus includes a calculator to calculate the viewing metric for the media based on the probabilities for the respective ones of the panelists and a sampling weight assigned to the respective ones of the panelists.

FIELD OF THE DISCLOSURE

This disclosure relates generally to media viewing metrics such asratings and shares and, more particularly, to methods and apparatus todetermine probabilistic media viewing metrics.

BACKGROUND

Audience viewership of, for example, a television program, may beanalyzed to determine ratings and/or shares for the program. Audienceviewing behavior data collected from, for example, a viewing panel, mayintroduce uncertainties into the analysis of the ratings and/or shares.For example there may be uncertainties as to whether a panelist iswatching television and, if so, what television channel or program thepanelist is watching.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates an example environment in which a system constructedin accordance with the teachings disclosed herein operates.

FIG. 2 is a block diagram of an example implementation of a portion ofthe system of FIG. 1.

FIG. 3 is a flowchart representative of example machine readableinstructions that may be executed to implement the example system ofFIGS. 1-2.

FIG. 4 illustrates an example processor platform that may execute theexample instructions of FIG. 3 to implement the example system of FIGS.1-2.

The figures are not to scale. Wherever possible, the same referencenumbers will be used throughout the drawing(s) and accompanying writtendescription to refer to the same or like parts.

DETAILED DESCRIPTION

Audience viewing data can be collected from a plurality of individualsor households watching, for example, television, to determine ratingsand/or shares for one or more television programs. Television ratingsrepresent a number of people (or households) with a television tuned toa particular channel or program divided by a total number of people (orhouseholds) that have a television. Thus, ratings consider a potentialviewing population, or the total number of people or households thathave a television. Television shares represent a percentage of people(or households) watching a particular channel or program out of aviewing population that includes the people (or households) that arewatching television at a given time. Thus, determining shares includesconsidering a population who is watching television at a given time.

When analyzing audience viewing behavior to calculate ratings and/orshares, there may be uncertainties with respect to whether a panelist(e.g., a person in a household selected to participate in ratingsresearch performed by, for example, The Nielsen Company (US), LLC) iswatching television and, if so, what television channel and/or programhe or she is watching. Uncertainties with respect to identifyingaudience viewing behavior can arise from, for example, co-viewing of atelevision program by members of the same household or a malfunction ofa television panel meter collecting viewing activity data from thepanelist's television. Thus, in some examples, viewing metrics such asratings and/or shares are determined using data including uncertaintiesor probabilities with respect to panelist viewing behavior.

For example, for a first panelist, there may be a 50% probability thatthe first panelist is not watching television or a 50% that the firstpanelist is watching a first program. As another example, data may becollected from a second panelist indicating that the second panelist iswatching television, but there may not be data as to which of a firstprogram, a second program, or a third program the second panelist iswatching. Known methods for addressing probabilities or uncertaintieswith respect to the viewing behavior of, for example, the first panelistand the second panelist include randomly assigning each panelist asviewing a particular television program using a Monte Carlo simulationor a variation thereof. For example, the first panelist who is eithernot watching television or is watching the first program may be randomlyassigned as watching the first program. The second panelist who iswatching one of the first program, the second program, or the thirdprogram may be randomly assigned to the second program. Thus, in someknown methods, each of the first panelist and the second panelist areassigned as watching a particular program or as not watching television(e.g., using “0's” and “1's”), thereby removing uncertainties from thepanelist data.

In some known methods, ratings and/or shares can be calculated based onthe randomly assigned probability data (e.g., the 0's and 1's) for thefirst panelist, the second panelist, and/or other panelists. However, insome known methods, a Monte Carlo simulation is only performed once. Asa result, ratings information does not account for the fact that thepanelists could be watching other programs probabilistically. Forexample, if the Monte Carlo simulation is performed multiple times, thesecond panelist could be randomly assigned as watching the first programor the third program instead of the second program. Thus, ratings and/orshares calculated based on random assignment of panelist viewingactivity may not accurately reflect a range of possible probabilisticscenarios, as the results are limited by the different scenarios thatare generated.

Accuracy of such known methods could be increased if, for example, theMonte Carlo simulation is performed multiple times (e.g., thousands oftimes) to identify a range of possible scenarios or outcomes withrespect to probabilities that a panelist is watching television, whatprogram a panelist is watching, etc. and if the ratings calculated fromthe different probabilistic scenarios are averaged. However, such knownmethods are time-consuming and can require significant processingresources to repeat the simulation thousands of times in an effort tocapture a wide range of possible probabilistic scenarios or outcomes.Even if the simulation is run multiple times, the results are stilllimited by the fact that ideally the simulation would be run an infinitenumber of times.

Examples disclosed herein provide for a determination of viewing metricssuch as ratings and/or shares that accounts for substantially allpossible viewing scenarios that could happen and a probability of aviewing scenario happening. For example, ratings computed using examplesdisclosed herein consider that the second panelist could be watching thefirst program, the second program, or the third program as well as therespective probabilities that the second panelist is watching the one offirst, second, or third programs. Examples disclosed herein computeratings and/or shares for one or more television programs using one ormore algorithms that consider the probabilities that a panelist may ormay not be watching television, may or may not be watching a certainprogram, etc. Some examples disclosed herein selectively adjust samplingweights assigned to a panelist in view of the probabilities that thepanelist is or is not watching television, is watching a certainprogram, etc. so as to identify a viewing population that can be used tocalculate, for example, shares despite the uncertainties in the data.

Some examples disclosed herein compute variance or covariance metricsfor analysis of viewing behavior across two or more television programs.Also, some disclosed examples can analyze ratings, shares, and/or otherviewing metrics for a population subgroup or panelist of interest. Forexample, a demographic group can be analyzed with respect to whatprogram the demographic group is watching or what portion of thedemographic group is watching a particular program.

Examples disclosed herein more accurately identify ratings and/or shareswith respect to uncertainties or probabilities in viewing behavior dataand reduce errors in computing ratings and/or shares as compared toapproaches that consider a limited range of probabilistic scenarios,only run a Monte Carlo simulation once, etc. Examples disclosed hereinimprove computational efficiency and reduce processing resources inconsidering the many scenarios that could arise for panelists or a groupof panelists. Examples disclosed herein substantially eliminate the needto run a probabilistic scenario simulation hundreds or thousands oftimes. Rather, examples disclosed herein generate results thatsubstantially approximate viewing metrics as if the simulations wereperformed an infinite number of times. Thus, disclosed examples providea technical improvement in the field of ratings metrics over knownmethods that address uncertainties in viewing data in a limited fashion.

Although examples disclosed herein are discussed in the context of mediaviewing metrics such as television ratings and/or shares, examplesdisclosed herein can be utilized in other applications. For example,examples disclosed herein could be used for other types of media thantelevision programs, such as radio. Also, examples disclosed hereincould be used in applications other than media to analyze behavior of apopulation with respect to, for example, buying a product such ascereal.

FIG. 1 illustrates an example system 100 for computing viewing metricssuch as ratings and/or shares associated with one or more televisionprograms. As illustrated in FIG. 1, a first household 102 includes afirst panelist 104. The first household 102 can include additionalpanelists. The first household 102 includes a first television 106. Afirst panel meter 108 is communicatively coupled to the first television106. The first television 106 can be tuned to broadcast one or morechannels 110 a-110 n. Each of the channels 110 a-110 n can provide oneor more media or programs 112 a-112 n to be viewed via the firsttelevision 106 by the first panelist 104.

The first panel meter 108 collects data from the first television 106,such as whether the first television 106 is turned on, to which of thechannels 110 a-110 n the first television is tuned, how long the firsttelevision 106 is tuned to the selected channel 110 a-110 n, what timeof day the first television 106 is tuned to the one of the channels 110a-110 n, etc. In the example of FIG. 1, the first panelist 104 isassociated with a plurality of demographics 114, such as age, gender,ethnicity, household size, etc. In some examples, the demographics 114include data about the geographic location of the first household 102,socioeconomic status, etc. In some examples, the first panel meter 108collects and/or stores data about the demographics 114 the firstpanelist 104 (e.g., via one or more user inputs with respect to thedemographics 114 of the first panelist 104, census data, etc.).

The example system 100 includes a second household 116. The secondhousehold 116 includes a second panelist 118. The second household caninclude additional panelists. The second household 116 includes a secondtelevision 120 and a second panel meter 122 communicatively coupled tothe second television 120. The second panel meter 122 collects data fromthe second television 120 regarding, for example, which of the channels110 a-110 n the second television 120 is tuned to at a given time ofday, and other data substantially as disclosed above in connection withthe first television 106 and the first panel meter 108. The second meter122 can collect and/or store data about demographics 124 associated withthe second panelist 118 (e.g., age, gender, etc. of the second panelist118).

The example system 100 can include other households in addition to thefirst household 102 and the second household 116 (e.g., n households102, 116). Also any of the households 102, 116 in the example system 100of FIG. 1 can include one or more panelists (e.g., n panelists 104,118). Television viewing activity can be collected from any of thehouseholds in the example system 100 substantially as described hereinwith respect to the first and second households 102, 116 of FIG. 1.

In the example system of FIG. 1, the first panel meter 108 and thesecond panel meter 122 are communicatively coupled to a processor 126(e.g., via wireless connections) to transmit return path data to theprocessor 126. The first panel meter 108 transmits a first data stream128 to the processor 126 including viewing data for the first television106 of the first household 102. The second panel meter 122 transmits asecond data stream 130 to the processor 126 including viewing data forthe second television 120 of the second household 102. The respectivedata streams 128, 130 can include data such as the channel(s) 110 a-110n to which each television 106, 120 is tuned at a certain time. Thefirst and second data streams 128, 130 can include demographic dataabout the panelists 104, 118 of the respective households 102, 116. Asdisclosed below, the processor 126 stores the data streams 128, 130 foranalysis with respect to television viewing metrics.

In some examples, the first data stream 128 and/or the second datastream 130 includes data indicative of one or more uncertainties aboutthe television viewing behavior of the first panelist 104 (or the firsthousehold 102) and/or the second panelist 118 (or the second household116). For example, there may be uncertainty as to whether the firstpanelist 102 was co-viewing one of the programs 112 a-112 n with anothermember of the first household 102. As another example, there may havebeen a temporary technical error in the collection of data by the firstand/or second panel meters 108, 122 (e.g., an inability to collect datafrom the television(s) 106, 120 for a period of time). Thus, at least aportion of the first data stream 128 and/or the second data stream 130may include uncertain or probabilistic viewing activity data by therespective panelists 104, 118 (and/or households 102, 116).

The example processor 126 of FIG. 1 includes a viewing activity analyzer132. The example viewing activity analyzer 132 calculates viewingmetrics such as ratings and/or shares for one or more of the programs112 a-112 n based on the data in the first data stream 128, the seconddata stream 130, and/or other data streams received from otherhouseholds in the example system 100. The example viewing activityanalyzer 132 considers any uncertainties in the first data stream 128and/or the second data stream 130 by calculating the viewing metricsusing one or more algorithms that account for probabilities with respectto whether or not the panelist(s) 104, 118 are watching television, whatprogram each panelist 104, 118 is watching, etc.

The example viewing activity analyzer 132 generates one or more viewingmetric outputs 134. The viewing metric output(s) 134 can include ratingsand/or shares for one or more of the programs 112 a-112 n. In someexamples, the viewing metric output(s) 134 can include analysis resultswith respect to viewing activity of a population subgroup of interest,such as a particular demographic subgroup (e.g., an age group). Theviewing metric output(s) 134 can be presented via one or more outputdevices 136, such as a display screen of a personal computing device(e.g., associated with the processor 126).

FIG. 2 is a block diagram of an example implementation of the viewingactivity analyzer 132 of FIG. 1. As illustrated in FIG. 2, the exampleviewing activity analyzer 132 includes a data collector 200. The exampledata collector 200 receives one or more of the data streams 128, 130from the panel meters 108, 122. As disclosed above, the data streams128, 130 include data such as date, time, and/or duration that thetelevision(s) 106, 120 were turned on; the channel(s) 110 a-110 n towhich the television(s) 106, 120 were tuned; the programs 112 a-112 nbroadcast by the channel(s) 110 a-110 n; the respective demographics114, 124 of the panelists 104, 118, etc. In some examples, the datacollector 200 filters and/or formats the data streams 128, 130 forprocessing by the viewing activity analyzer 132. The data streams 128,130 received by the data collector 200 are stored in a database 202 ofthe example viewing activity analyzer 132 of FIG. 2.

The example viewing activity analyzer 132 includes a sampling weightassigner 204. The example sampling weight assigner 204 assigns asampling weight 205 to each panelist 104, 118 based on, for example, therespective demographics 114, 124 of each panelist 104, 118. The samplingweight(s) 205 assigned by the example weight assigner 204 to eachpanelist 104, 118 is indicative of a number of other television viewersthat each panelist 104, 118 represents based on, for example, one ormore similar demographics 114, 124 (e.g., age, gender, socioeconomicstatus). For example, if the sampling weight assigner 204 assigns asampling weight 205 having a value of ten to the first panelist 104, thefirst panelist 104 represents ten people sharing similar demographics114 as the first panelist 104.

In some examples, the sampling weight 205 is based on whether the panelmeter(s) 108, 122 were working properly during a time period in whichthe data of the data stream(s) 128, 130 was collected. For example, if aknown power outage affected the first household 102 and, thus, theability of the first panelist 104 to watch the first television 106 andthe first panel meter 108 to collect data, the example sampling weightassigner 204 can adjust the sampling weight 205 assigned to the firstpanelist 104 to reflect a number of people who were affected by thepower outage.

In the example of FIG. 2, the sampling weight(s) 205 assigned to thepanelist(s) 104, 118 can be based on one or more sampling weight rule(s)206 stored in the database 202 of FIG. 2. The sampling weight rules 206can include one or more rules with respect to a value of the samplingweight(s) 205 to be assigned to each panelist 104, 118 based ondemographic factors such as age, gender, household size, etc. Theexample sampling weight assigner 204 of FIG. 2 compares the demographicdata 114, 124 in the data streams 128, 130 to the sampling weightrule(s) 206 to determine the sampling weight(s) 205 to assign to thepanelist(s) 104, 118.

The example viewing activity analyzer 132 of FIG. 2 includes aprobability identifier 208. The example probability identifier 208analyzes the first and second data streams 128, 130 to identify anyuncertainties in the data streams 128, 130. For example, the probabilityidentifier 208 can identify missing data in the first and/or second datastreams 128, 130 with respect to, for example, data regarding whether ornot the panelist(s) 104, 118 where watching the television(s) 106, 120,what program(s) 112 a-112 n the panelist(s) 104, 118 were watching, etc.The probability identifier 208 can identify inconsistencies in the firstand/or second data streams 128 such as data corresponding to one or moreprogram(s) 112 a-112 n that did not air during the time period for whichthe data was collected. The probability identifier 208 can identifypotential co-viewing activity based on, for example, a number ofpanelists 104, 118 associated with each household 102, 116.

In other examples, the probability identifier 208 does not identify anyuncertainties in the first and/or second data streams 128, 130. Forexample, the data stream(s) 128, 130 can include data with respect tothe television program(s) 112 a-112 n that the panelist(s) 104, 118 werewatching that has not been affected by, for example, any technicalerrors in the data collection.

In some examples, the probability identifier 208 assigns one or moreviewing probabilities 209 to the panelist(s) 104, 118 based on theuncertainties identified in the data stream(s) 128, 130 with respect to,for example, whether or not the panelist(s) 104, 118 are watchingtelevision, what program(s) 112 a-112 n the panelist(s) 104, 118 couldhave watched, etc. The example probability identifier 208 assigns theprobabilities 209 based on one or more probability rules 207 stored inthe example database 202 of FIG. 2. The probability rules 207 caninclude predefined rules with respect to probability values to beassigned to the panelists 104, 118 based on, for example, the number ofprograms 112 a-112 n that the panelist(s) 104, 118 could be watching ata given time, the sampling weights 205 assigned to the panelist(s) 104,118, historical viewing data for the respective panelist(s) 104, 118stored in the database 202, etc.

Table 1, below, is an example table generated by the example probabilityidentifier 208 of FIG. 2. Table 1 includes probabilistic viewingactivity for a plurality of panelists (e.g., the panelists 104, 118 ofFIG. 1) whose viewing data is received by the data collector 200 of theexample viewing activity analyzer 132. Table 1 includes theprobabilistic viewing activity with respect to a first program 112 a(P_(112a)), a second program 112 b (P_(112b)), and a third first program112 c(P_(112c)). Table 1 also includes probabilities with respect towhether or not the panelists are watching television (P₀).

TABLE 1 Viewing Activity Probabilities Age (e.g., Sampling demographicsWeights Panelist 114, 124) (205) P₀ P_(112a) P_(112b) P_(112c) A (e.g.,Young 10 0.5 .5 0 0 panelist 104) B (e.g., Young 60 0 .33 .33 .33panelist 118) C Young 20 1 0 0 0 D Middle 80 .1 .2 .3 .4 E Middle 40 0 01 0 F Middle 70 0 .3 .5 .2 G Old 90 .25 .25 .25 .25 H Old 30 .4 .3 .2 .1I Old 50 .1 .7 0 .2

As illustrated above, the example Table 1 includes panelist identifiers(e.g., letters A-H), associated demographics (e.g., age), and respectivesampling weights 205 assigned to the panelists (e.g., by the samplingweight assigner 204 of the viewing activity analyzer 132). In exampleTable 1, the values in the third column P₀ represent a probability thata respective panelist is not watching television, the values in thefourth column P_(112a) represent a probability that a panelist iswatching the first program 112 a, the values in the fifth columnP_(112b) represent a probability that a panelist is watching the secondprogram 112 b, and the value in the sixth column P_(112c) represent aprobability that a panelist is watching the third program 112 c.

For example, referring to Table 1, the probability identifier 208determines based on the first data stream 128 that Panelist A (e.g., thefirst panelist 104 of FIG. 1) is either not watching television with a50% probability or watching the first program 112 a with a 50%probability.

As another example, the probability identifier 208 determines based on,for example, the second data stream 130, that Panelist B (e.g., thesecond panelist 118 of FIG. 1) is watching television. However, theprobability identifier 208 is unable to determine which program 112 a,112 b, 112 c Panelist B is watching based on the second data stream 130.Accordingly, the probability identifier 208 assigns equal probabilitiesto Panelist B with respect to the first, second, and third programs 112a, 112 b, 112 c. As another example, the probability identifier 208 candetermine that Panelist E is watching the second program 112 b based ona data stream received by the data collector 200 for Panelist E.Accordingly, the probability identifier 208 assigns Panelist E aprobability of “1” based on the data indicating that Panelist E iswatching the first program 112 a. Thus, as disclosed above, the exampleprobability identifier 208 analyzes the data streams (e.g., the datastreams 128, 130) and assigns probabilities 209 with respect to viewingactivity based on the data, including any uncertainties in the data.

The example viewing activity analyzer 132 of FIG. 2 includes a ratingscalculator 210. The example ratings calculator 210 calculates one ormore ratings 211 for one or more of the programs 112 a, 112 b, 112 cbased on the data in the data streams (e.g., the data streams 128, 130)in view of the probabilities 209 determined by the probabilityidentifier 208 (e.g., as provided in Table 1). In the example of FIG. 2,the ratings calculator 210 also determines a null rating 211representative of a percent of panelists not watching television (e.g.,F₀). The example ratings calculator 210 of FIG. 2 employs a plurality ofalgorithms that account for the sampling weights 205 assigned to therespective panelists by the sampling weight assigner 204 and theprobabilities 209 assigned by the probability identifier 208.

For example, the ratings calculator 210 can apply the followingequations to determine the expected ratings 211 for the first, second,and third programs 112 a, 112 b, 112 c and the percent of televisionsnot tuned to any of the programs 112 a, 112 b, 112 c:

Where p_(k,i) is a probability that the k^(th) panelist is watching thei^(th) program, w_(k) is a sampling weight associated with the k^(th)panelist, and n is the number of panelists,

$\begin{matrix}{{E\left\lbrack R_{i} \right\rbrack} = \frac{\sum\limits_{k = 1}^{n}{w_{k}p_{k,i}}}{\sum\limits_{k = 1}^{n}w_{k}}} & (1) \\{{{Var}\left\lbrack R_{i} \right\rbrack} = \frac{\sum\limits_{k = 1}^{n}{{w_{k}^{2}\left( {1 - p_{k,i}} \right)}p_{k,i}}}{\left( {\sum\limits_{k = 1}^{n}w_{k}} \right)^{2}}} & (2) \\{{{Cov}\left\lbrack {R_{i},R_{j}} \right\rbrack} = {- \frac{\sum\limits_{k = 1}^{n}{w_{k}^{2}p_{k,i}p_{k,j}}}{\left( {\sum\limits_{k = 1}^{n}w_{k}} \right)^{2}}}} & (3)\end{matrix}$

Thus, expected ratings, variance, and covariance calculations are summedacross the number of panelists n (e.g., the Panelists A-H of Table 1,above). In some examples, the ratings calculator 210 utilizes anormalized sampling weight or weighted average v_(k) for the samplingweights 205 associated with the panelists, where

$v_{k} = {\frac{w_{k}}{\sum\limits_{k = 1}^{n}w_{k}}.}$

Equations 1-3 above can be modified to include the normalized weightv_(k) as follows:

E[R _(i)]=Σ_(k=1) ^(n) v _(k) p _(k,i)  (4)

Var[R _(i)]=Σ_(k=1) ^(n) v _(k) ²(1−p _(k,i))p _(k,i)  (5)

Cov[R _(i) ,R _(j)]=−Σ_(k=1) ^(n) v _(k) ² p _(k,i) p _(k,j)  (6)

In Equation (4), above, the expected ratings 211 for the i^(th) program(e.g., one of programs 112 a, 112 b, 112 c) are determined by summingthe weighted average v_(k) by the probability that the panelists (and,thus, the number of people each panelist represents) are watching thei^(th) program.

In Equation (5), above, the variance calculation accounts for aprobability that, for example, Panelist A (e.g., the first panelist 104of FIG. 1) is not watching television and a probability that Panelist Ais watching the i^(th) program (e.g., the first program 112 a). Thus,Equation (5) accounts for uncertainties in the first data stream 128with respect to whether or not the first panelist 104 is watching thefirst program 112 a (e.g., p_(k,i)) or is not watching television (e.g.,1−p_(k,i))) by considering both probabilities.

Equation (5) also considers the sampling weight 205 assigned to PanelistA (e.g., the first panelist 104) and, accordingly, a portion of thepopulation represented by the Panelist A. For example, as indicated inexample Table 1, above, the Panelist A is assigned a weight of ten.Thus, Panelist A represents ten individuals sharing, for example, asimilar age demographic as Panelist A. As such, if there is a 20%probability that Panelist A is watching the first program 112 a, thenthe ten people represented by the Panelist A are also considered to bewatching the first program 112 a with a probability of 20%. Thus,Equation (5) considers the probability that Panelist A is watchingtelevision and/or is watching one of the programs 112 a, 112 b, 112 c aswell as the portion of the population represented by the first panelist104. In Equation (5), the variance is summed across the panelists toaccount for the fact that different panelists are associated withdifferent probabilities of viewing a program and/or differentprobabilities with respect to not viewing television.

Referring to Table 1 above including the probabilities 209 of televisionviewership activity, the example ratings calculator 210 calculates theratings 211 for the first program 112 a, the second program 112 b, andthe third program 112 c using Equations (1) or (4). The ratingscalculator 210 also calculates a null rating 211 representing apercentage of panelists not watching television. For example, theratings calculator 210 can calculate the following expected ratings 211for P₀, P_(112a), P_(112b), P_(112c) of Table 1 as follows:

E[R _(i)]=[0.1611 0.2855 0.3274 0.2259]  (7)

Also, the example ratings calculator 210 can calculate a covariancematrix σ²(R_(i),R_(j)) based on the variance equations (e.g., Equations(2) or (5)) and the covariance equations (e.g., Equations (3) or (6)) asfollows:

$\begin{matrix}{{\sigma^{2}\left( {R_{i}R_{j}} \right)} = \begin{pmatrix}{+ 0.0126} & {- 0.0047} & {- 0.0038} & {- 0.0042} \\{- 0.0047} & {+ 0.0253} & {- 0.0103} & {- 0.0103} \\{- 0.0038} & {- 0.0103} & {+ 0.0248} & {- 0.0108} \\{- 0.0042} & {- 0.0103} & {- 0.0108} & {+ 0.0253}\end{pmatrix}} & (8)\end{matrix}$

The covariance matrix (8) indicates relationships between, for example,the first program 112 a and the other programs 112 b, 112 c. In theexample covariance matrix (8), the diagonals of the matrix are computedby the ratings calculator 210 based on the variance (e.g., Equations (2)or (5)) and the off-diagonals of the matrix are computed based on thecovariance (e.g., Equations (3) or (6)). In the example covariancematrix (8), the off-diagonals include negative values. The negativevalues of the off-diagonals in the covariance matrix (8) reflect thefact out of the potential viewing population, more people in thepopulation who are watching one program (e.g., the first program 112 a)means that less people in the population are able to watch the otherprograms (e.g., the second program 112 b, the third program 112 c).Also, the ratings calculator 210 considers the population that may notbe watching television because that population is a part of the totalpotential viewing population. Thus, the example ratings calculator 210of FIG. 2 calculates the ratings for the first, second, and thirdprograms 112 a, 112 b, 112 c based the probabilities that the panelists(and, thus, the portion of the population they represent) are viewingtelevision or not viewing television.

The example viewing activity analyzer 132 of FIG. 2 includes a sharecalculator 212. The share calculator 212 determines share(s) 213, or apercentage of televisions that are in use that are tuned to a certainprogram. The shares computed by the example share calculator 212 areconditional based on the panelists (e.g., the panelists 104, 118 ofFIG. 1) who are watching television. As disclosed above, there may beuncertainties with respect to whether a panelist such as the firstpanelist 104 and/or the second panelist 118 is watching television.Thus, the number of panelists who watching are television is a randomvariable. The shares calculator 212 considers the different panelistswho may be watching television, as each panelist's sampling weight 205may differ from another panelist.

The random variables with respect to the number of panelists who arewatching television and the different sampling weights 205 associatedeach panelist can consume extensive resources of a processor (e.g., theprocessor 126 of FIG. 1) to calculate exact shares values. For example,to calculate the exact shares values, the shares calculator 212 wouldneed to run multiple simulations considering all of the programs 112a-112 n the panelists could be watching, with different paneliststreated as watching different programs for each simulation. The multiplesimulations consume resources of the processor 126, which can increase atime to perform the analysis and decrease efficiency. However, theshares calculator 212 of FIG. 2 increases the efficiency in determiningthe share(s) 213 by approximating the share(s) 213 as a conditionaldistribution of ratings. In the example of FIG. 2, the calculation ofthe share(s) 213 based on the conditional distribution of ratingsconverges to the exact shares values as the number of panelistsconsidered increases. For a large panel size (e.g., thousands ofpanelists), the difference between the shares 213 calculated by theshares calculator 212 based on the conditional distribution and theexact shares values (e.g., calculated based on multiple simulations withthe panelists watching different programs in each simulation) issubstantially negligible.

The example shares calculator 212 of FIG. 2 determines a probabilitythat a panelist is watching a particular program (e.g., the first,second, or third programs 112 a, 112 b, 112 c), on the condition thatthe panelist is watching television. The shares calculator 212calculates a share weight 215 for each panelist (e.g., the panelists104, 118 of FIG. 1) based on a product of the sampling weight 205assigned to the panelist and a probability that the panelist is notviewing television. The shares calculator 212 calculates a normalizedshare weight z_(k) based on the sampling weights 205 (e.g., the samplingweights 205 in Table 1) as follows:

$\begin{matrix}{z_{k} = \frac{w_{k}\left( {1 - p_{k,0}} \right)}{\sum\limits_{k = 1}^{n}{w_{k}\left( {1 - p_{k,0}} \right)}}} & (9)\end{matrix}$

Equation (9) adjusts the respective sampling weights 205 assigned to thepanelists based on the probabilities p_(k,0) that the panelists are notwatching television. The shares calculator 212 calculates a conditionalshare probability that if a panelist is watching television, then thepanelist is watching the i^(th) program, as follows:

$\begin{matrix}{s_{k,i} = \frac{p_{k,i}}{1 - p_{k,0}}} & (10)\end{matrix}$

In the example of FIG. 2, the shares calculator 212 generates a tableincluding share weights 215 for each panelist in Table 1 (above) andconditional probabilities with respect to whether each panelist watchingthe first, second, or third programs 112 a, 112 b, 112 c Table 2, below,is an example table generated by the shares calculator 212 based onEquations (9) and (10) for the panelists in Table 1:

TABLE 2 Conditional Share Probabilities Age (e.g., Share demographicsWeights Panelist 114, 124) (215) S₁ S₂ S₃ A (e.g., Young 5 1 0 0panelist 104) B (e.g., Young 60 .333 .333 .333 panelist 118) C Young 0N/A N/A N/A D Middle 72 .222 .333 .444 E Middle 40 0 1 0 F Middle 70 .3.5 .2 G Old 67.5 .333 .333 .333 H Old 18 .5 .333 .166 I Old 45 .777 0.222

For example, in Table 1, above, Panelist C is assigned a sampling weight205 of 20 by the example weight assigner 204 of FIG. 2 (e.g., based ondemographics associated with Panelist C). However, Panelist C is alsoassigned a value of 1 with respect to P₀, indicating that Panelist C isnot watching television. Accordingly, the example shares calculator 212adjusts the sampling weight 205 assigned to Panelist C such thatPanelist C has a share weight 215 of 0 because Panelist C is notwatching television. As illustrated in example Table 2, because PanelistC is not watching television, Panelist C does not contribute to thecalculation of the shares 213 for the first, second, and/or thirdprograms 112 a, 112 b, 112 c.

As another example, in Table 1, Panelist A is assigned a 50% probabilityof not watching television and a 50% probability of watching the firstprogram 112 a. Accordingly, the example shares calculator 212 adjuststhe share weight 215 assigned to Panelist A in Table 2. Also, theexample shares calculator 212 determines a conditional share probabilityindicating that if Panelist A is watching a program, then Panelist A iswatching the first program 112 a (e.g., as indicated by the value “1”for S₁).

As another example, Table 1 indicates that there is a 10% probabilitythat Panelist D is not watching television. Thus, there is a 90%probability that Panelist D is watching television. The example sharescalculator 212 of FIG. 2 adjusts the sampling weight 205 (e.g., 80)assigned to Panelist D to obtain the share weight 215 for Panelist D(e.g., 80*0.9=72). Thus, although for ratings purposes, Panelist Drepresents 80 people, for purposes of determining shares, Panelist Drepresents 72 people. As also indicated in Table 1, there is a 20%probability that Panelist D is watching the first program 112 a, a 30%probability of watching the second program 112 b, and a 40% probabilityof watching the third program 112 c, and, thus, a 90% probability thatPanelist D is watching one of the programs 112 a, 112 b, 112 c. Theshares calculator 212 calculates, for example, a conditional shareprobability S₁ that Panelist D is watching the first program 112 a basedon the probability that Panelist D is watching the first program fromTable 1 (e.g., 0.2/0.9=0.222). The shares calculator 212 calculates aconditional share probability S₂ that Panelist D is watching the secondprogram 112 b (e.g., 0.3/0.9=0.333) and a conditional share probabilityS₃ that Panelist D is watching the third program 112 b (e.g.,0.4/0.9=0.444). Thus, the conditional share probabilities S₁, S₂, S₃ inTable 2 are based on the condition that a panelist is viewingtelevision.

The examples shares calculator 212 of FIG. 2 computes the expectedshares for the ith program (e.g., first, second, and/or third programs112 a, 112 b, 112 c), the variance, and covariance based on the data inexample Table 2 as follows:

E[S _(i)]=Σ_(k=1) ^(n) z _(k) s _(k,i)  (11)

Var[S _(i)]=Σ_(k=1) ^(n) z _(k) ²(1−s _(k,i))s _(k,i)  (12)

Cov[R _(i) ,R _(j)]=−Σ_(k=1) ^(n) z _(k) ² s _(k,i) s _(k,j)  (13)

In some examples, if the ratings for the ith program (e.g., first,second, and/or third programs 112 a, 112 b, 112 c) have been calculated(e.g., as disclosed above with respect to Equations (1) or (4)), theshares calculator 212 calculates the expected shares as follows:

$\begin{matrix}{{E\left\lbrack S_{i} \right\rbrack} = \frac{E\left\lbrack R_{i} \right\rbrack}{1 - {E\left\lbrack R_{0} \right\rbrack}}} & (14)\end{matrix}$

The expected shares E[S_(i)] computed by the example shares calculator212 represents the condition probability that given that the panelist iswatching television, then the panelist and, thus, the persons thepanelist represents, is watching the ith program (e.g., first, second,or third programs 112 a, 112 b, 112 c).

Referring to Table 2 above including the probabilities of viewershipactivity with respect to the first, second, and/or third programs 112 a,112 b, 112 c, the example shares calculator 212 calculates the expectedshares 213 for the first program 112 a, the second program 112 b, andthe third program 112 c using Equations (11) or (14). For example, theshares calculator 212 can calculate the following expected shares 213for first, second, and/or third programs 112 a, 112 b, 112 c as follows:

E[S _(i)]=[0.3404 0.3907 0.2689]  (15)

Also, the example shares calculator 212 can calculate a covariancematrix σ²(S_(i), S_(j)) based on the variance (e.g., Equation (12)) andthe covariance (e.g., Equation (13)) for Table 2 as follows:

$\begin{matrix}{{\sigma^{2}\left( {S_{i}S_{j}} \right)} = \begin{pmatrix}0.0293 & {- 0.0146} & {- 0.0147} \\{- 0.0146} & 0.0299 & {- 0.0153} \\{- 0.0147} & {- 0.0153} & 0.0300\end{pmatrix}} & (16)\end{matrix}$

The covariance matrix (16) indicates relationships between, for example,the first program 112 a and the other programs 112 b, 112 c. In theexample covariance matrix (16), the diagonals of the matrix (16) arecomputed by the shares calculator 212 based on the variance (e.g.,Equation (12)) and the off-diagonals of the matrix are computed based onthe covariance (e.g., Equation (13)). In the example covariance matrix(16), the off-diagonals include negative values. The negative values ofthe off-diagonals in the covariance matrix (16) reflect the fact out ofthe population who is viewing television, more people in the populationwho are watching one program (e.g., the first program 112 a) means thatless people in the population are watching the other programs (e.g., thesecond program 112 b, the third program 112 c). Thus, the example sharescalculator 212 of FIG. 2 calculates the shares for the first, second,and third programs 112 a, 112 b, 112 c based the probabilities that thepanelists (and, thus, the population the panelists represent) areviewing the television and viewing certain programs.

Thus, the ratings calculator 210 and the shares calculator 212 of theexample viewing activity analyzer 132 of FIG. 2 determines ratingsand/or shares for one or more of the programs 112 a-112 n that may beviewed by panelist, such as the first panelist 104 and/or the secondpanelist 118 of FIG. 1. As disclosed above, each of the panelists 104,118 is associated with respective demographics 114, 124. The exampleviewing activity analyzer 132 of FIG. 2 can also calculate the ratingsand/or shares for the program(s) 112 a-112 n based on a subgroup ofinterest, such as a subgroup associated with a particular demographic(e.g., age, gender).

The example viewing activity analyzer of FIG. 2 includes a subgroupanalyzer 214. In some examples, a user of the example processor 126 ofFIG. 1 can request that the ratings calculator 210 of the viewingactivity analyzer 132 calculate ratings 211 for one or more of theprograms 112 a-112 n for a particular demographic group (e.g., byproviding a user input to the processor 126). Additionally oralternatively, the user can request that the shares calculator 212calculate shares 213 for one or more of the programs 112 a-112 n for aparticular demographic group. The example subgroup analyzer 214identifies the relevant demographics 114, 124 of the data streams 128,130 stored in the example database 202 of the viewing activity analyzer132. The subgroup analyzer 214 provides the relevant demographic data tothe ratings calculator 210 and/or the shares calculator 212.

For example, referring to Table 1 above, a user may be interested inratings 211 and shares 213 for one or more of the programs 112 a-112 nfor just the “young” demographic group. Based on a user input receivedby the processor 126 directing the viewing activity analyzer 132 todetermine the ratings for the “young” demographic group, the examplesubgroup analyzer 214 identifies the relevant data streams 128, 130stored in the database 202 corresponding to the demographic group ofinterest. For example, with respect to the “young” demographic group,the subgroup analyzer 214 identifies the viewing data associated withPanelist A (e.g., the first panelist 104), Panelist B (e.g., the secondpanelist 118), and Panelist C based on their association with thedemographic group of interest. In some examples, the subgroup analyzer214 scans the data stored in the database 202 to identify the relevantpanelist viewing data based on, for example, tags associated with thedata stream 128, 130 stored in the database 202.

The example subgroup analyzer 214 provides the relevant viewing data forthe demographic group of interest to the ratings calculator 210 and theshares calculator 212. The example ratings calculator 210 of FIG. 2applies one or more of Equations (1)-(6) above to determine the expectedrating(s) 211 for the programs(s) 112 a-112 n for the selecteddemographic group. For example, the ratings calculator 210 performs thesummations for only the demographic group of interest (e.g.,E[R_(i)]=Σ_(k=1)v_(k)p_(k,i), where n is the number of panelists in the“young” demographic group). In some examples, the ratings calculator 210determines normalized weights (e.g., the weight v_(k)) for thedemographic group of interest based on the sampling weights 205 assignedto the panelists associated with the demographic group of interest. Therating calculator 210 uses the normalized weights to calculate theexpected ratings, variance, and/or covariance for the demographic groupof interest.

Similarly, the example shares calculator 212 of FIG. 2 calculates theshare(s) 213 for the program(s) 112 a-112 n using the normalized weightsfor the demographic group of interest and by summing across the numberof panelists in the demographic group of interest to calculate theexpected share(s) 213, variance, and/or covariance (e.g., usingEquations (9)-(14)). Thus, the example viewing activity analyzer 132 candetermine expected ratings and/or shares and respective variance andcovariance of the ratings and/or shares for a subgroup of interest.

The example subgroup analyzer 214 can also determine one or moresubgroup viewing metrics 217. For example, the subgroup analyzer 214 candetermine a probability that a person within a demographic group ofinterest is watching a particular program 112 a-112 n (e.g. in responseto user input received by the processor 126). For example, a user may beinterested in a probability that a person in the “middle” demographicage group of Table 1 is watching the one of the programs 112 a, 112 b,112 c. In such examples, the example subgroup analyzer 214 of FIG. 2identifies Panelists D, E, and F as associated with the “middle” agegroup and generates a vector K including viewing data for Panelists D,E, and F from the respective data streams stored in the database 202.For example, based on the data in the vector K, the subgroup analyzer214 can determine the probability that any person within the “middle”age group is watching i^(th) program as follows:

Prob[K∈ith program]=1−Π_(k∈K)(1−p_(k,i)) (17), where Prob[K∈ith program]is the probabitlity at least one person in the subgroup of interest iswatching the i^(th) program and (1−p_(k,i)) is the probability a personin the subgroup is not watching the i^(th) program.

Thus, Equation (17) calculates a product over members of the selectedsubgroup with respect to the subgroup members watching a program ofinterest.

For example, referring to Table 1, the probability identifier 208identified a 20% probability that Panelist D is watching the firstprogram 112 a, a 0% probability that Panelist E is watching the firstprogram 112 a, and a 30% probability that Panelist F is watching thefirst program 112 a. The subgroup analyzer 214 can determine theprobability that one of Panelists D, E, or F are watching the firstprogram 112 a as follows:

Prob[“Middle” age group watching firstprogram]=1−(1−0.2)(1−0)(1−0.3)=0.44  (18)

Thus, the subgroup analyzer 214 determines that there is a 44%probability that a panelist (and, thus, the persons the panelist(s)represent) in the “middle” age demographic is watching the first program112 a. Also, subgroup analyzer 214 can determine the variance asfollows:

Var[X]=(Π_(k∈K)(1−p _(k,i)))(1−Π_(k∈K)(1−p _(k,i)))  (19)

The example subgroup analyzer 214 of FIG. 2 can also determine for agiven program 112 a-112 n, a percentage of people watching the programwho are associated with a certain demographic. In the example of FIG. 2,data regarding the number of panelists in a demographic who are viewingthe program 112 a-112 n of interest and the number of total peopleviewing the program 112 a-112 n of interest are random variables. Thesubgroup analyzer 214 analyzes different probabilistic combinations ofgroups of panelists (e.g., the panelists in Table 1) who are watchingthe program 112 a-112 n of interest and the respective sampling weights205 assigned to the panelists. In some examples, the subgroup analyzer214 approximates the percentage of panelists in a demographic group ofinterest who are watching the program 112 a-112 n of interest based on alarge panel size (e.g., thousands of panelists). For example, for agroup of K people, the subgroup analyzer 214 can approximate aproportion of panelists watching program i that belong to the group K asfollows:

$\begin{matrix}{p_{\{ K\}} = \frac{\sum\limits_{k \in K}{w_{k}p_{k,i}}}{\sum\limits_{k = 1}^{n}{w_{k}p_{k,i}}}} & (20)\end{matrix}$

In Equation (20), above, the numerator represents the subgroup ofinterest and the denominator considers all panelists viewing the programof interest (e.g., all demographics). The subgroup analyzer 214 candetermine the variance and covariance as follows:

$\begin{matrix}{{{Var}\left\lbrack p_{{\{ K\}},i} \right\rbrack} = \frac{\sum\limits_{k \in K}{{w_{k}^{2}\left( {1 - p_{k,i}} \right)}p_{k,i}}}{\left( {\sum\limits_{k = 1}^{n}{w_{k}p_{k,i}}} \right)^{2}}} & (21) \\{{{Cov}\left\lbrack {p_{{\{ K\}},i},p_{{\{ K\}},j}} \right\rbrack} = {- \frac{{\sum\limits_{k \in K}{w_{k}^{2}p_{k,i}}},p_{k,j}}{\left( {\sum\limits_{k = 1}^{n}{w_{k}p_{k,i}}} \right)\left( {\sum\limits_{k = 1}^{n}{w_{k}p_{k,j}}} \right)}}} & (22)\end{matrix}$

The covariance determined by Equation (22) can be used to analyzeviewing activity for different programs 112 a-112 n across the subgroupof interest. For example, the covariance can be analyzed with respect toa proportion of viewers belonging to a subgroup across two differentprograms 112 a-112 n.

The example viewing activity analyzer 132 can calculate the ratings 211,the shares 213, and/or the subgroup viewing metrics 217 at the householdlevel in addition or as an alternative to determining viewing metrics atthe panelist level or demographic group level. For example, the samplingweight assigner 204 can assign sampling weights 205 to the firsthousehold 102 and/or the second household 116 based on, for example,household size. Based on a user request to calculate, for example,ratings 211 and/or shares 213 at the household level, the subgroupanalyzer 214 can identify and/or format the viewing data of the datastreams 128, 130 by household. As an example, the ratings calculator 210can determine the ratings 211 based on a probability that any member ofthe household (e.g., the first household 102) is watching television.

Thus, the example viewing activity analyzer 132 can determine differentviewing activity metrics such as ratings 211 and/or shares 213 despiteprobabilities or uncertainties in the data streams (e.g., the datastreams 128, 130 of FIG. 1) received from the panel meters (e.g., themeters 108, 122). The example viewing activity analyzer 132 can alsodetermine subgroup-specific metrics, including, for example, whatprogram(s) a demographic group is watching and/or what demographic groupis watching a certain program. The example viewing activity analyzer 132includes a communicator 216. The communicator 216 outputs one or more ofthe ratings 211, shares 213, or subgroup metrics (e.g., the viewingmetric output(s) 134 of FIG. 1) for display via, for example, the outputdevice 136.

While an example manner of implementing the viewing activity analyzer132 is illustrated in FIGS. 1-2, one or more of the elements, processesand/or devices illustrated in FIGS. 1-2 may be combined, divided,re-arranged, omitted, eliminated and/or implemented in any other way.Further, the example data collector 200, the example database 202, theexample sampling weight assigner 204, the example probability identifier208, the example ratings calculator 210, the example shares calculator212, the example subgroup analyzer 214, the example communicator 216and/or, more generally, the example viewing activity analyzer of FIGS.1-2 may be implemented by hardware, software, firmware and/or anycombination of hardware, software and/or firmware. Thus, for example,any of the example data collector 200, the example database 202, theexample sampling weight assigner 204, the example probability identifier208, the example ratings calculator 210, the example shares calculator212, the example subgroup analyzer 214, the example communicator 216and/or, more generally, the example viewing activity analyzer of FIGS.1-2 could be implemented by one or more analog or digital circuit(s),logic circuits, programmable processor(s), application specificintegrated circuit(s) (ASIC(s)), programmable logic device(s) (PLD(s))and/or field programmable logic device(s) (FPLD(s)). When reading any ofthe apparatus or system claims of this patent to cover a purely softwareand/or firmware implementation, at least one of the example datacollector 200, the example database 202, the example sampling weightassigner 204, the example probability identifier 208, the exampleratings calculator 210, the example shares calculator 212, the examplesubgroup analyzer 214, the example communicator 216 and/or, moregenerally, the example viewing activity analyzer of FIGS. 1-2 is/arehereby expressly defined to include a tangible computer readable storagedevice or storage disk such as a memory, a digital versatile disk (DVD),a compact disk (CD), a Blu-ray disk, etc. storing the software and/orfirmware. Further still, the example data collector 200, the exampledatabase 202, the example sampling weight assigner 204, the exampleprobability identifier 208, the example ratings calculator 210, theexample shares calculator 212, the example subgroup analyzer 214, theexample communicator 216 and/or, more generally, the example viewingactivity analyzer of FIGS. 1-2 may include one or more elements,processes and/or devices in addition to, or instead of, thoseillustrated in FIGS. 1-2, and/or may include more than one of any or allof the illustrated elements, processes and devices.

A flowchart representative of example machine readable instructions forimplementing the example viewing activity analyzer 132 of FIGS. 1-2 isshown in FIG. 3. In this example, the machine readable instructionscomprise a program for execution by a processor such as the processor126 of FIG. 1 and shown in the example processor platform 400 discussedbelow in connection with FIG. 4. The program may be embodied in softwarestored on a tangible computer readable storage medium such as a CD-ROM,a floppy disk, a hard drive, a digital versatile disk (DVD), a Blu-raydisk, or a memory associated with the processor 126, but the entireprogram and/or parts thereof could alternatively be executed by a deviceother than the processor 126 and/or embodied in firmware or dedicatedhardware. Further, although the example program is described withreference to the flowchart illustrated in FIG. 3, many other methods ofimplementing the example viewing activity analyzer 132 of FIGS. 1-2 mayalternatively be used. For example, the order of execution of the blocksmay be changed, and/or some of the blocks described may be changed,eliminated, or combined.

As mentioned above, the example process of FIG. 3 may be implementedusing coded instructions (e.g., computer and/or machine readableinstructions) stored on a tangible computer readable storage medium suchas a hard disk drive, a flash memory, a read-only memory (ROM), acompact disk (CD), a digital versatile disk (DVD), a cache, arandom-access memory (RAM) and/or any other storage device or storagedisk in which information is stored for any duration (e.g., for extendedtime periods, permanently, for brief instances, for temporarilybuffering, and/or for caching of the information). As used herein, theterm “tangible computer readable storage medium” is expressly defined toinclude any type of computer readable storage device and/or storage diskand to exclude propagating signals and to exclude transmission media. Asused herein, “tangible computer readable storage medium” and “tangiblemachine readable storage medium” are used interchangeably. Additionallyor alternatively, the example process of FIG. 3 may be implemented usingcoded instructions (e.g., computer and/or machine readable instructions)stored on a non-transitory computer and/or machine readable medium suchas a hard disk drive, a flash memory, a read-only memory, a compactdisk, a digital versatile disk, a cache, a random-access memory and/orany other storage device or storage disk in which information is storedfor any duration (e.g., for extended time periods, permanently, forbrief instances, for temporarily buffering, and/or for caching of theinformation). As used herein, the term non-transitory computer readablemedium is expressly defined to include any type of computer readablestorage device and/or storage disk and to exclude propagating signalsand to exclude transmission media. As used herein, when the phrase “atleast” is used as the transition term in a preamble of a claim, it isopen-ended in the same manner as the term “comprising” is open ended.

The program 300 of FIG. 3 begins at block 302 with the data collector200 of the example viewing activity analyzer 132 of FIG. 2 accessing oneor more data streams such as the first data stream 128 and/or the seconddata stream 130 of FIG. 1 from the panel meter(s) 108, 122 associatedwith televisions 106, 120 in one or more households 102, 116 (block302). The data stream(s) 128, 132 include television viewing data withrespect to, for example, a program 112 a-112 n broadcast by thetelevision(s) 106, 120 and viewed by the panelists 104, 118. The datacan be stored in the example database 202 of the example viewingactivity analyzer of FIG. 2.

The program of FIG. 3 includes the example sampling weight assigner 204of FIG. 2 assigning sampling weight(s) 205 to the panelist(s) 104, 118(block 304). The sampling weight assigner 204 can assign the samplingweight(s) 205 based on, for example, one or more demographics 114, 124associated with the panelist(s) 104, 118, such as age and/or gender. Insome examples, the sampling weight assigner 204 assigns samplingweight(s) 205 to the household(s) 102, 116 from which the data stream(s)218, 130 are received based on, for example, household size. Thesampling weight assigner 204 can assign the sampling weight(s) 205 basedon one or more sampling weight rule(s) 206 stored in the exampledatabase 202 of the viewing activity analyzer 132 of FIG. 2.

The program of FIG. 3 includes the probability identifier 208determining viewing probabilities 209 for, for example, the panelist(s)104, 116 associated with data stream(s) 128, 130 (block 306). Theprobability identifier 208 identifies uncertainties in the datastream(s) 128, 130 with respect to, for example, whether a panelist iswatching television, what program 112 a-112 n the panelist is watching,etc. In some examples, the uncertainties are due to, for example,potential co-viewing activity between two or more members of ahousehold. In other examples, the uncertainties are due to, for example,a technical error in the collection of the viewing data by the panelmeter(s) 108, 122. The probability identifier 208 can determine theviewing probabilities 209 with respect to whether or not a panelistwatched television and/or what program(s) 112 a-112 n the panelist couldhave watched based on one or more probability rule(s) 207 stored in theexample database 202 of FIG. 2. In some examples, the probabilityidentifier 208 identifies the probabilities 209 with respect to, forexample, whether or not any member of a household is watchingtelevision.

The program of FIG. 3 includes the example ratings calculator 210 ofFIG. 2 calculating expected ratings 211 for one or more programs 112a-112 n (block 308). In some examples, the ratings calculator 210 usesone or more algorithms to calculate the ratings 211, such as Equations(1) or (4) disclosed above. In determining the ratings 211, the ratingscalculator 210 accounts for the probabilities 209 with respect towhether or not the panelist(s) 104, 118 are watching television, whatprogram(s) 112 a-112 n the panelist(s) 104, 118 are watching, etc. Insome examples, the ratings calculator 210 calculates the variance (e.g.,using Equations (2), (5)) and/or covariance (e.g., using Equations (3),(6)) with respect to program viewing activity to analyze viewershipbehavior between, for example, two or more programs 112 a-112 n (e.g.,as reflected in the example covariance matrix (8)). In some examples,the ratings calculator 210 calculates a null rating 211 indicative of apercentage of panelists who are not watching any program.

In some examples of the program of FIG. 3, the shares calculator 212 ofFIG. 2 additionally or alternatively calculates the expected share(s)213 for the program(s) 112 a-112 n (e.g., using Equation (11) disclosedabove) (block 308). For example, to calculate the share(s) 213, theexample shares calculator 212 adjusts the sampling weight(s) 205assigned to the panelist(s) 104, 118 to determine share weight(s) 215representative of television viewing behavior by the panelist(s) 104,118 (e.g., based on probabilities 209 indicating that the panelist(s)104, 118 may or may not be watching television). The example sharescalculator 212 calculates the shares 213 based on the share weights 215and conditional probabilities that the panelist(s) are watching aparticular program 112 a-112 n, if the panelist(s) are watchingtelevision (e.g., determined based on the probabilities 209 with respectto program viewing probabilities). In some examples, the sharescalculator 212 calculates the variance (e.g., using Equation (12))and/or covariance (e.g., using Equation (13)) with respect to programviewing activity to analyze viewing activity between, for example, twoor more programs 112 a-112 n (e.g., as reflected in the examplecovariance matrix (16)).

The example of FIG. 3 includes a determination as to whether the examplesubgroup analyzer 214 of FIG. 2 is to calculate one or more subgroupviewing metrics 217 (block 310). In some examples, the subgroup analyzer214 calculates the subgroup viewing metric(s) 217 based on one or moreuser inputs received via the processor 126 of FIG. 1 that instructsviewing metrics such as ratings 211 and/or shares 213 to be calculatedfor one or more demographic groups of interest (e.g., an age group, anethnic group, a gender group).

The subgroup analyzer 214 identifies viewing data for the subgroup ofinterest based on the data streams 128, 130 stored in the database 202of FIG. 2 (block 312). In some examples, the subgroup analyzer 214identifies the relevant viewing data for panelists in the subgroup ofinterest (e.g., the panelists 104, 118 of FIG. 1) based on one or moretags identify the demographics 114, 124 associated with the panelists.

The example of FIG. 3 includes calculating the one or more subgroupviewing metrics 217 (block 314). In some examples, the subgroup analyzer214 instructs the ratings calculator 210 to calculate ratings 211 forone or more programs 112 a-112 n for the subgroup of interest. In someexamples, the subgroup analyzer 214 instructs the shares calculator 212to calculate shares 213 for one or more programs 112 a-112 n for thesubgroup of interest. In such examples, the ratings calculator 210calculates the ratings 211 (and, in some examples, the variance andcovariance) substantially as disclosed above (e.g., at block 308) forthe subgroup of interest. Also in some such examples, the sharescalculator 212 calculates the shares 213 and, in some examples, thevariance and covariance) substantially as disclosed above (e.g., atblock 308) for the subgroup of interest.

In some examples, the subgroup analyzer 214 calculates subgroup viewingmetrics 217 with respect to, for example, a probability that a subgroupof interest is watching one or more of the programs 112 a-112 n. Forexample, the subgroup analyzer 214 uses Equation (17), disclosed above,to determine a probability that any person within a demographic group ofinterest is watching one of the programs 112 a-112 n. In some examples,the subgroup analyzer 214 determines a subgroup that is watching aparticular program 112 a-112 n. For example, the subgroup analyzer 214uses Equation (20), disclosed above, to approximate a proportion ofpanelists watching one of the programs 112 a-112 n that belong to asubgroup of interest (e.g., a demographic group of interest).

If a decision is made not to calculate viewing metrics for a subgroup(e.g., at block 310), the example program 300 ends. Also, if there areno further subgroup viewing metrics 217 to calculate (e.g., based onuser input(s) received at the processor 126), the example program 300ends.

FIG. 4 is a block diagram of an example processor platform 400 capableof executing the instructions of FIG. 3 to implement the data collector200, the example database 202, the example sampling weight assigner 204,the example probability identifier 208, the example ratings calculator210, the example shares calculator 212, the example subgroup analyzer214, the example communicator 216 and/or, more generally, the exampleviewing activity analyzer of FIGS. 1-2. The processor platform 400 canbe, for example, a server, a personal computer, a mobile device (e.g., acell phone, a smart phone, a tablet such as an iPad™), a personaldigital assistant (PDA), an Internet appliance, a set top box, or anyother type of computing device.

The processor platform 400 of the illustrated example includes theprocessor 126. The processor 126 of the illustrated example is hardware.For example, the processor 126 can be implemented by one or moreintegrated circuits, logic circuits, microprocessors or controllers fromany desired family or manufacturer.

The processor 126 of the illustrated example includes a local memory 413(e.g., a cache). The processor 126 of the illustrated example is incommunication with a main memory including a volatile memory 414 and anon-volatile memory 416 via a bus 418. The volatile memory 414 may beimplemented by Synchronous Dynamic Random Access Memory (SDRAM), DynamicRandom Access Memory (DRAM), RAMBUS Dynamic Random Access Memory (RDRAM)and/or any other type of random access memory device. The non-volatilememory 416 may be implemented by flash memory and/or any other desiredtype of memory device. Access to the main memory 414, 416 is controlledby a memory controller.

The processor platform 400 of the illustrated example also includes aninterface circuit 420. The interface circuit 420 may be implemented byany type of interface standard, such as an Ethernet interface, auniversal serial bus (USB), and/or a PCI express interface.

In the illustrated example, one or more input devices 422 are connectedto the interface circuit 420. The input device(s) 422 permit(s) a userto enter data and commands into the processor 126. The input device(s)can be implemented by, for example, an audio sensor, a microphone, acamera (still or video), a keyboard, a button, a mouse, a touchscreen, atrack-pad, a trackball, isopoint and/or a voice recognition system.

One or more output devices 136, 424 are also connected to the interfacecircuit 420 of the illustrated example. The output devices 136, 424 canbe implemented, for example, by display devices (e.g., a light emittingdiode (LED), an organic light emitting diode (OLED), a liquid crystaldisplay, a cathode ray tube display (CRT), a touchscreen, a tactileoutput device, a printer and/or speakers). The interface circuit 420 ofthe illustrated example, thus, typically includes a graphics drivercard, a graphics driver chip or a graphics driver processor.

The interface circuit 420 of the illustrated example also includes acommunication device such as a transmitter, a receiver, a transceiver, amodem and/or network interface card to facilitate exchange of data withexternal machines (e.g., computing devices of any kind) via a network426 (e.g., an Ethernet connection, a digital subscriber line (DSL), atelephone line, coaxial cable, a cellular telephone system, etc.).

The processor platform 400 of the illustrated example also includes oneor more mass storage devices 428 for storing software and/or data.Examples of such mass storage devices 428 include floppy disk drives,hard drive disks, compact disk drives, Blu-ray disk drives, RAIDsystems, and digital versatile disk (DVD) drives.

Coded instructions 432 to implement the instructions of FIG. 3 may bestored in the mass storage device 428, in the volatile memory 1014, inthe non-volatile memory 416, and/or on a removable tangible computerreadable storage medium such as a CD or DVD.

From the foregoing, it will be appreciated that the above disclosedsystems, methods, and apparatus improves the ability to determineviewing metrics such as ratings and/or shares for media such as one ormore television programs in view of uncertainties or probabilities inthe data from which the viewing metrics are calculated. Examplesdisclosed herein determines the viewing metrics by accounting fordifferent scenarios with respect to whether a panelist is watchingtelevision, what program he or she is watching, etc. and theprobabilities that such scenarios will happen. Examples disclosed hereincompute expected ratings and/or expected shares and respective varianceor covariance thereof despite the probabilities in the viewing data.Thus, examples disclosed herein compute ratings and/or shares that moreaccurately reflect viewer behavior as compared to ratings and/or sharescalculated based on the randomly assigned probability data (e.g., the0's and 1's).

Examples disclosed herein increase efficiency and reduce processorresources in determining the ratings and/or shares based on theprobabilistic data as compared to, for example, repeating probabilisticstimulations thousands of times, by approximating expected ratingsand/or shares. Some disclosed examples provide for calculation ofsubgroup-specific metrics. Disclosed examples provide accurate andefficient analyses of viewing behavior despite uncertainties orprobabilities in the viewing data.

Although certain example methods, apparatus and articles of manufacturehave been disclosed herein, the scope of coverage of this patent is notlimited thereto. On the contrary, this patent covers all methods,apparatus and articles of manufacture fairly falling within the scope ofthe claims of this patent.

1. An apparatus for determining a viewing metric for media to be viewedby a plurality of panelists, the apparatus comprising: a probabilityidentifier to identify a probability for respective ones of thepanelists with respect to the panelists viewing the media, theprobability identifier to identify the probability based on viewing datafor the respective ones of the panelists, the viewing data includingincomplete viewing data for one or more of the panelists relative to themedia; and a calculator to: calculate a conditional probability for therespective ones of the panelists based on the probability for therespective ones of the panelists; and approximate the viewing metricusing a conditional distribution based on the conditional probabilityand a sampling weight assigned to the respective ones of the panelists.2. The apparatus of claim 1, wherein the media is first media, theprobability is a first probability for the respective ones of thepanelists, and the probability identifier is to identify a secondprobability for the respective ones of the panelists with respect to thepanelists viewing second media, the calculator to: calculate the viewingmetric for the second media; and determine a covariance between thefirst media and the second media based on the respective viewing metricsfor the first media and the second media.
 3. The apparatus of claim 1,wherein the calculator is to calculate a rating for the media.
 4. Theapparatus of claim 1, wherein the viewing metric is a share for themedia, the calculator to further calculate the conditional probabilitybased on a probability of the respective ones of the panelists viewing atelevision broadcasting the media.
 5. The apparatus of claim 1, furtherincluding a subgroup analyzer, the subgroup analyzer to identify therespective probabilities for a subgroup including one or more of thepanelists with respect to the panelists of the subgroup viewing themedia based on one or more demographics of the respective panelists. 6.The apparatus of claim 5, wherein the subgroup analyzer is to determinea probability of the subgroup viewing the media based on theprobabilities identified for the subgroup.
 7. The apparatus of claim 5,wherein the subgroup analyzer is to determine a portion of the panelistsviewing the media who are associated with the subgroup based on theprobabilities identified for the subgroup and the probabilitiesidentified for all of the panelists.
 8. A method for determining aviewing metric for media to be viewed by a plurality of panelists, themethod comprising: identifying, by executing an instruction with aprocessor, a probability for respective ones of the panelists withrespect to the panelists viewing the media, the identifying based onviewing data for the respective ones of the panelists, the viewing dataincluding incomplete viewing data for one or more of the panelistsrelative to the media; and calculating, by executing an instruction withthe processor, a conditional probability for the respective ones of thepanelists based on the probability for the respective ones of thepanelists; and approximating, by executing an instruction with theprocessor, the viewing metric using a conditional distribution based onthe conditional probability and a sampling weight assigned to therespective ones of the panelists.
 9. The method of claim 8, wherein themedia is first media, the probability is a first probability for therespective ones of the panelists, and further including: identifying asecond probability for the respective ones of the panelists with respectto the panelists viewing second media; calculating the viewing metricfor the second media; and determining a covariance between the firstmedia and the second media based on the respective viewing metrics forthe first media and the second media.
 10. The method of claim 8, furtherincluding calculating a rating for the media.
 11. The method of claim 8,wherein the viewing metric is a share for the media and furtherincluding calculating the conditional probability for the media based ona probability of the respective ones of the panelists viewing atelevision broadcasting the media.
 12. The method of claim 8, furtherincluding identifying the respective probabilities for a subgroupincluding one or more of the panelists with respect to the panelists ofthe subgroup viewing the media based on one or more demographics of therespective panelists.
 13. The method of claim 12, further includingdetermining a probability of the subgroup viewing the media based on theprobabilities identified for the subgroup.
 14. The method of claim 12,further including determining a portion of the panelists viewing themedia who are associated with the subgroup based on the probabilitiesidentified for the subgroup and the probabilities identified for all ofthe panelists.
 15. A tangible computer-readable medium comprisinginstructions that, when executed, cause a processor to at least:identify a probability for respective ones of panelists with respect tothe panelists viewing a media, the processor to identify the probabilitybased on viewing data for the respective ones of the panelists, theviewing data including incomplete viewing data for one or more of thepanelists relative to the media; and calculate a conditional probabilityfor the respective ones of the panelists based on the probability forthe respective ones of the panelists; and approximate the viewing metricusing a conditional distribution based on the conditional probability asampling weight assigned to the respective ones of the panelists. 16.The computer-readable medium of claim 15, wherein the media is firstmedia, the probability is a first probability for the respective ones ofthe panelists, and the instructions further cause the processor to:identify a second probability for the respective ones of the panelistswith respect to the panelists viewing second media; calculate theviewing metric for the second media; and determine a covariance betweenthe first media and the second media based on the respective viewingmetrics for the first media and the second media.
 17. Thecomputer-readable medium of claim 15, wherein the viewing metric is ashare for the media and the instructions further cause the processor tocalculate the conditional probability based on a probability of therespective ones of the panelists viewing a television broadcasting themedia.
 18. The computer-readable medium of claim 15, where theinstructions further cause the processor to identify the respectiveprobabilities for a subgroup including one or more of the panelists withrespect to the panelists of the subgroup viewing the media based on oneor more demographics of the respective panelists.
 19. Thecomputer-readable medium of claim 18, wherein the instructions furthercause the processor to determine a probability of the subgroup viewingthe media based on the probabilities identified for the subgroup. 20.The computer-readable medium of claim 18, wherein the instructionsfurther cause the processor to a portion of the panelists viewing themedia who are associated with the subgroup based on the probabilitiesidentified for the subgroup and the probabilities identified for all ofthe panelists.